Problem 63 - Chemistry The Science in Context

Question

The manufacture of aluminum includes the production of cryolite (Na_AIF_ ) from the following reaction: \(6 \mathrm{HF}(g)+3 \mathrm{NaAlO}_{2}(s) \rightarrow \mathrm{Na}_{3} \mathrm{AlF}_{6}(s)+3 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s)\). How much NaAlO, (sodium aluminate) is required to produce \(1.00 \mathrm{kg}\) of \(\mathrm{Na}_{3} \mathrm{AlF}_{6} ?\)

Step-by-Step Solution

Answer

Answer: Approximately 1.17 kg of sodium aluminate (NaAlO2) is required to produce 1.00 kg of cryolite (Na3AlF6).

Step 1: Calculate the moles of Na3AlF6 (cryolite)

Given the mass of cryolite (1.00 kg) we need to calculate the number of moles. We need to find the molar mass of Na3AlF6 to do this: Molar mass of Na3AlF6 = (3 x Molar mass of Na) + (1 x Molar mass of Al) + (6 x Molar mass of F) = (3 x 22.99 g/mol) + (1 x 26.98 g/mol) + (6 x 18.998 g/mol) = 209.94 g/mol Now that we have the molar mass of Na3AlF6, we can convert mass to moles: moles of cryolite = (mass of cryolite) / (molar mass of Na3AlF6) = (1000 g) / (209.94 g/mol) = 4.762 mol

Step 2: Find the mole ratio between NaAlO2 and Na3AlF6

From the balanced equation, we can see that the mole ratio between NaAlO2 and Na3AlF6 is: 3 NaAlO2 : 1 Na3AlF6 This means that 3 moles of NaAlO2 are required to produce 1 mole of Na3AlF6.

Step 3: Calculate the moles of NaAlO2 required

Using the mole ratio, we can now calculate the number of moles of NaAlO2 required to produce 4.762 moles of Na3AlF6: moles of NaAlO2 = (moles of Na3AlF6) x (3 moles of NaAlO2 / 1 mole of Na3AlF6) = 4.762 mol x 3 = 14.29 mol

Step 4: Convert moles of NaAlO2 to mass

To find out how much sodium aluminate is required, we need to convert the moles of NaAlO2 back to mass. First, we'll calculate the molar mass of NaAlO2: Molar mass of NaAlO2 = (1 x Molar mass of Na) + (1 x Molar mass of Al) + (2 x Molar mass of O) = (1 x 22.99 g/mol) + (1 x 26.98 g/mol) + (2 x 15.999 g/mol) = 81.96 g/mol Now, we'll convert moles of NaAlO2 to mass: mass of NaAlO2 = (moles of NaAlO2) x (molar mass of NaAlO2) = 14.29 mol x 81.96 g/mol = 1171.95 g So, 1171.95 g (or approximately 1.17 kg) of sodium aluminate (NaAlO2) is required to produce 1.00 kg of cryolite (Na3AlF6).

Key Concepts

Mole Concept

Understanding the mole concept is essential in the realm of chemistry. The term 'mole' refers to a standard unit of measurement used within chemistry to express amounts of a chemical substance. One mole of any substance contains exactly 6.022 x 10²³ (Avogadro's number) of particles, whether they are atoms, molecules, ions, or electrons.

This concept becomes particularly useful when dealing with chemical reactions because it allows chemists to predict the amounts of substances consumed and produced in a reaction. In the given problem, we are concerned with the amount of sodium aluminate needed to produce a kilogram of cryolite. By calculating the number of moles of cryolite and using the stoichiometry of the given chemical reaction, we can find out the moles of sodium aluminate required.

One common issue students encounter is not clearly understanding the relationship between moles, molar mass, and the number of particles. Remember, molar mass is the bridge between the mass of a substance and the amount in moles. By mastering the mole concept, you'll be able to tackle a wide range of problems in chemistry with confidence.

Chemical Reactions

Chemical reactions are the processes by which chemical substances transform into new substances. These reactions are described by chemical equations that provide a symbolic representation of the reactants and products involved in the reaction, as well as their quantities.

For understanding any chemical reaction, like the formation of cryolite, it's important to look at the balanced chemical equation. It shows how many moles of each reactant are needed to create a specific amount of product. In the exercise, the equation tells us that three moles of sodium aluminate react with six moles of hydrofluoric acid to produce one mole of cryolite, three moles of water, and one mole of aluminum oxide.

Enhancing Relative Proportion Understanding

Enhancing students' understanding of relative proportions in chemical reactions can be achieved by emphasizing mole-to-mole comparisons. This approach involves using the coefficients in the balanced chemical equation to deduce the ratio and then applying this ratio to find out how much of another substance is needed. These stoichiometric relationships are at the heart of predicting the outcome of chemical reactions.

Molar Mass Calculation

The molar mass of a substance is the mass in grams of one mole of that substance. It is a physical property that is usually expressed in units of grams per mole (g/mol). It's equivalent to the atomic or molecular mass of a substance when measured in atomic mass units (amu).

To solve problems in stoichiometry, like the exercise given, you must calculate the molar mass of the substances involved in the reaction. For cryolite (Na₃AlF₆), the calculation includes adding the molar masses of sodium (Na), aluminum (Al), and fluorine (F) based on their respective mole ratios in the formula.

Breaking Down Complex Calculations

When it comes to improving students' comprehension of molar mass calculations, it's beneficial to break down complex formulas into simpler components. Teach students to identify the individual elements in a compound and then compute the molar mass by adding the mass contributions from each element based on their subscript numbers in the formula. By doing so, they will find the calculation less daunting and be able to apply these skills to various chemical substances with different complexities.